Find two irrational numbers between 0.12 and 0.13
Let a = 0.12 and b = 0.13.
Clearly, a and b are rational numbers such that a < b.
We observe that the number a and b have a 1 in the first place of decimal. But in the second place of decimal a has a 2 and b has 3. So, we consider the numbers
c = 0.1201001000100001 …… and, d = 0.12101001000100001…….
Clearly, c and d are irrational numbers such that a < c < d < b.
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- Proofs of Irrationality